The overall goal of the proposed project is to optimize bone-implant systems while taking into account statistical distributions in environmental variables, such as loading on the prosthesis and bone tissue properties adjacent to the prosthesis. To date, optimal designs of implants have not considered the effects of observed variations in loading and bone properties that occur from individual to individual, and in a single individual over time. If conventional search techniques are used, the optimal design of total joint replacements is computationally expensive, particularly if variation in the loading and material property distributions are included. If the effects of bone remodeling and in vivo changes in implant materials and interfaces are included, the computational demands are even greater. Therefore, new methods must be employed. The primary goal of the proposed research is to establish and validate general methodology for evaluating the optimal design of orthopaedic systems that involve large-scale, nonlinear computational analyses. As a secondary goal, and as an example of the usefulness of the methodology, the robustness of optimal designs of uncemented femoral components for total hip replacements will be determined, taking into account environmental variations in loading and bone properties. Specifically, the applicants will determine the strategy in statistical methodology for designing computer experiments that will maximize the efficiency of these methods for the optimal design of total joint replacements. They will first validate these methods using in vitro experiments. They will then apply these methods to determine the design of an anatomical femoral component for a total hip replacement that minimizes the load bypass (stress shielding) in the proximal femur for distributions to the prosthesis. Finally, they will use the methodology to determine the robustness of the optimal designs for more strenuous loading conditions than those that occur during gait, and for bone properties that are substantially different from those that occur in the normal population due to aging or disease.